Inertial sensors are a cornerstone of modern (high bandwidth) navigation systems. Inertial sensors can be described as inertial measurement units (IMU). Typical IMUs include one or more gyroscopic sensors to detect a magnitude and direction of angular change and a plurality of accelerometers to determine accelerations in three dimensions. IMU sensor data can be integrated to determine velocity and position of an object or vehicle containing the IMU sensor. IMUs offer a means to “black box” dead reckoning, but suffer from significant difficulties in terms of sensor errors. A gyroscope bias offset, for example, results in accrued orientation error, which in turn results in incorrect gravity compensation of acceleration measurements. When these errors are integrated, significant positioning error is quickly accrued.
Dynamic calibration of inertial sensors can be a vital aspect of inertial navigation. The current state-of-the-art relies upon various Kalman filtering architectures to produce an in-situ estimate of sensor errors. Sensor error estimates are often fed back, much like a control loop, to compensate for sensor errors in real-time before integration is performed.
Simultaneous localization and mapping (SLAM) has been a major area of navigation-related research over the past two decades. The development of sparse methods have allowed a new perspective on navigation and localization, bringing into question whether Kalman filtering is the best way of inferring inertial sensor calibration parameters.
Localization and mapping strategies developed in recent years have primarily focused on cameras or laser scanners as primary navigation sensors. SLAM has been extensively studied by the robotics community and some efforts have converged toward a factor graph representation of robot localization and mapping measurements. Many of the existing prior art focuses on visual (monocular and/or stereo) aiding only.
Leutenegger et al. (S. Leutenegger et al. “Keyframe-based visual-inertial odometry using nonlinear optimization,” The International Journal of Robotics Research, December 2014) published work on a visual inertial SLAM solution, which estimates bias terms. Their work presents an overview of visual inertial systems, but does not present complete analytical models for compensated interpose inertial constraints.
Indelman et al. (V. Indelman, et al. “Factor graph based incremental smoothing in inertial navigation systems,” in Intl. Conf. on Information Fusion (FUSION), Singapore, July 2012, pp. 2154-2161) initially proposed to use individual inertial sensor measurements for odometry constraints, creating a new pose for each sensor measurement. However, the rapid increase in the number of poses makes it difficult to compute real-time solutions for large problems. Later work has adopted pre-integrals, but fails to present an analytical version of an inertial sensor model.
Martinelli (A. Martinelli, “Vision and IMU data fusion: Closed-form solutions for attitude, speed, absolute scale, and bias determination,” Robotics, IEEE Transactions on, vol. 28, no. 1, pp. 44-60, February 2012) proposed a closed-form solution for visual-inertial odometry constraints, but only considered accelerometer biases during his derivation. While accelerometer bias is an important error source, it is not the most significant. Platform misalignment, which is predominantly driven by gyroscope bias, results in erroneous coupling of gravity compensation terms. This gravity misalignment, when integrated, is a dominant error source in all inertial navigation systems.
Monocular SLAM, bundle adjustment, and structure from motion (SfM) show that images from a single moving camera can provide sufficient information for localization and mapping. The solution, however, has unconstrained scale. Some SLAM solutions, such as LSD-SLAM, explicitly parameterize map scale and must be inferred by other means.
In 2001, Qian et al (G. Qian, R. Chellappa, and Q. Zheng, “Robust structure from motion estimation using inertial data,” JOSA A, vol. 18, no. 12, pp. 2982-2997, 2001) suggested incorporating inertial data with a structure from motion procedure to aid in scale observability. This data fusion further enables high-resolution trajectory estimation between camera frames and coasting through featureless image sequences. However, these methods do not model raw sensor error terms, and in effect require high-performance IMUs or ultimately incur little dependence on poor inertial measurements.
There have been some attempts in the prior art (such as T. Lupton et al., “Visual-inertial-aided navigation for high-dynamic motion in built environments without initial conditions,” IEEE Trans. Robotics, vol. 28, no. 1, pp. 61-76, February 2012) in which raw inertial measurements are integrated first and offset compensation is only done later. However, there exists a need for continuous propagation and closed-form solution. There remains a need to perform more optimal in-situ inference over inertial measurements for localization, mapping and control, in a manner similar to how one would use “non-differentiated” measurements such as landmark sightings or range measurements
A strong synergy between visual and inertial sensors has resulted in various visual-inertial navigation systems (VINS) being developed. Major contributions to visual-inertial odometry came in 2007 with the introduction of the Multi-State Constrained Kalman Filter (MSC-KF) by Mourikis et al. (A. I. Mourikis et al., “A multi-state constraint Kalman filter for vision-aided inertial navigation,” in Robotics and Automation, 2007 IEEE International Conference on. IEEE, 2007, pp. 3565-3572) and inertial structure from motion by Jones et al. (E. Jones et al., “Visual-inertial navigation, mapping and localization: A scalable real-time causal approach,” The International Journal of Robotics Research, vol. 30, no. 4, pp. 407-430, 2011.) Both employ tight coupling between inertial measurements and visual feature tracking. The visually aided inertial navigation by Madison et al. (R. W. Madison, et al., “Vision-aided navigation for small UAVs in gps-challenged environments,” The Draper Technology Digest, p. 4, 2008) uses a loosely coupled Kalman filter to fuse visual and inertial information.
Refinements to the MSC-KF have improved filter consistency by restricting the state updates to respect the unobservable null space of the system, which enters the state through linearization assumptions and numerical computational issues. Filtering style VINS generally estimate a single snapshot estimate of inertial sensor biases. One notable issue with visual inertial filtering solutions is that both the prediction and measurement models are non-linear. It has been noted that performance may be improved by improving linearization points through iteration of the updates to the state vector. Since filter update steps are in essence Gauss-Newton updates steps, the work of Bell (B. M. Bell, “The iterated Kalman smoother as a gauss-newton method,” SIAM Journal on Optimization, vol. 4, no. 3, pp. 626-636, 1994) stands a good middle ground between filtering and smoothing solutions.
The aerospace community has contributed significantly to in-situ navigation and converged on an extended Kalman filter (EKF) data fusion architecture for inertial navigation systems (INS). Groves (P. D. Groves, Principles of GNSS, inertial, and multisensor integrated navigation systems. Artech House, GNSS Technology and Application Series, 2008) argued that any aided inertial navigation system should always estimate gyroscope and accelerometer biases. Industrial applications commonly use Kalman filters to dynamically estimate a single time-slice of 30 or more IMU calibration parameters.
A common approach is to use inertial sensors for capturing high bandwidth dynamics and gravity measurements while radio-based ranging measurements, such as a global navigation satellite system (GNSS), preserve the long term accuracy of the navigation solution. GNSS aiding is either done by cascading the INS/GNSS filter behind the GNSS solution filter (loosely coupled), or directly using pseudo-range satellite measurements in the INS/GNSS measurement model (tightly coupled). In the extreme, inertial information is used to also aid satellite signal tracking (deeply coupled). Today, variations of these filtering techniques are used for both manned and unmanned aerial vehicles. Maritime and underwater navigation use a similar processing architecture, although there is more emphasis on acoustic navigational aids.
While much of the work in this field has focused on visual filtering methods, there remains a need for improved bias compensation for IMUs.